Solve 3x-5yb=5x+2

$$3 x - 5 y b = 5 x + 2$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{2\left(x+1\right)}{5y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&x=-1\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$-5yb=5x+2-3x$$

Combine 5x and -3x to get 2x.

$$-5yb=2x+2$$

The equation is in standard form.

$$\left(-5y\right)b=2x+2$$

Divide both sides by -5y.

$$\frac{\left(-5y\right)b}{-5y}=\frac{2x+2}{-5y}$$

Dividing by -5y undoes the multiplication by -5y.

$$b=\frac{2x+2}{-5y}$$

Divide 2+2x by -5y.

$$b=-\frac{2\left(x+1\right)}{5y}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{2\left(x+1\right)}{5y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&x=-1\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$-5yb=5x+2-3x$$

Combine 5x and -3x to get 2x.

$$-5yb=2x+2$$

The equation is in standard form.

$$\left(-5y\right)b=2x+2$$

Divide both sides by -5y.

$$\frac{\left(-5y\right)b}{-5y}=\frac{2x+2}{-5y}$$

Dividing by -5y undoes the multiplication by -5y.

$$b=\frac{2x+2}{-5y}$$

Divide 2+2x by -5y.

$$b=-\frac{2\left(x+1\right)}{5y}$$

Solve for x

$$x=-\frac{5by}{2}-1$$

Steps for Solving Linear Equation

Subtract 5x from both sides.

$$3x-5yb-5x=2$$

Combine 3x and -5x to get -2x.

$$-2x-5yb=2$$

Add 5yb to both sides.

$$-2x=2+5yb$$

The equation is in standard form.

$$-2x=5by+2$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{5by+2}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{5by+2}{-2}$$

Divide 2+5yb by -2.

$$x=-\frac{5by}{2}-1$$